A person can row 8 km upstream and 24 km downstream in 4 hours. He can row 12 km downstream and 12 km upstream in 4 hours. Find the speed of the person in still water as also the speed of the current
Answers
LET SPEED OF BOAT IN STILL WATER BE X AND THAT OF CURRENT BE Y (BOTH IN KMPH)
TIME = DISTANCE / SPEED
SO 8/(X-Y)+24/(X+Y)=4 OR 2/P+6/Q=1 WHERE P=X-Y Q=X+Y
ALSO 12/(X+Y)+12/(X-Y)=4 OR 3/P+3/Q=1
SOLVING THE EQUATIONS WE HAVE P=4 Q=12
SO X=8 Y=4
SO SPEED OF PERSON IN STILL WATER IS 8 KMPH AND THAT OF CURRENT IS 4 KMPH
Answer:
Y = 4 and X = 8
Step-by-step explanation:
Let the speed of rowing in still water = x km/hr
Let the speed of current = y km/hr
Speed of boat in upstream is (x - y) km/hr
Speed of boat in downstream is (x + y) km/hr
Distance = Speed x time
Time = Distance/Speed
Thus, the equations will be:
8/(x-y) + 24/(x + y) = 4 ............ (1)
12/(x-y) + 12/(x + y) = 4 ............ (2)
Now the above equations will be reduced in linear form
Let 1/(x-y) = A
and 1/(x+y) = B
So the new equations will be:
8A + 24B = 4 ............(3)
12A + 12B = 4 ............(4)
On multiplying eq. (4) by 2 and then subtracting from eq. (3), we get
-16A = -4
A = 1/4 --------- (5)
On putting value of "A" in eq. (4) , we get,
3 + 12 B = 4
B = 1/12 ------------ (6)
Now we know that A = 1/( x-y) and B = 1/(x+y)
On putting values of "A" and "B" we get:
1/( x-y) = 1/4
( x-y) = 4 ---------- (7)
1/( x+y)= 1/12
x + y = 12 ------- (8)
On adding eq. (7) and (8), we get:
2x = 16
x = 8 ----- (9)
On putting value of "x" in eq. (8), we get
y = 4